Preheat the oven to 180C/350F and spray a 9x13 inch pan with cooking spray. Place a wide strip of grease proof paper into the pan with enough overhang over the sides to pick the cake up.
Place the sugar, butter and lemon zest into a large bowl, or the bowl of your stand mixer, and beat until light and fluffy; 2 minutes on medium-high speed.
Add in the eggs, scraping down the sides as necessary, and mix on medium speed until well combined and smooth.
Place the flour, baking powder, bicarbonate of soda, salt and cranberries into a medium sized bowl and stir until all the cranberries are coated in flour.
Tip the flour mixture into your egg mixture and mix on low until the mixture starts to come together, then add in the milk and continue to mix on medium speed until everything is well combined and smooth.
Tip the batter into your prepared pan and smooth into an even layer with a spatula/wooden spoon.
Place in the oven for 22-27 minutes (mine took 25 exactly) until risen, golden and an inserted skewer into the centre comes out clean.
Leave to cool completely before making the frosting: Place the icing sugar and butter into a large bowl and beat on low speed with a hand mixer until all the sugar is mixed with the butter. You may have lumps of butter at this stage, add in the lemon juice 1tsp at a time, mixing after each addition until the frosting comes together, then add the milk if required. Turn the speed up to high and beat for a good 3 minutes, the frosting will pale in colour and get light and fluffy. You want a thick frosting which you can spread, but it should hold its shape.
Lift the cake out of the pan and transfer to a cutting board: spoon the frosting into the centre of the cake and then use a small angled spatula to spread the frosting over the top of the cake.
Sprinkle with lemon zest if you want to and then slice into 16-20 cake bars. Lemon and Cranberry Cake Bars will keep in an airtight container, in the fridge for 4 days. Best served at room temperature.